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Q. ${ }^{14} C _7+\displaystyle\sum_{i=1}^3{ }^{17- i } C _6=$

NTA AbhyasNTA Abhyas 2022

Solution:

$14C_{7}+\displaystyle \sum _{i = 1}^{3}{}^{17 - i}C_{6}^{}$
$^{14}C_{7}+{}^{14}C_{6}^{}+{}^{15}C_{6}^{}+{}^{16}C_{6}^{}$
$={}^{15}C_{7}^{}+{}^{15}C_{6}^{}+{}^{16}C_{6}^{}$
$={}^{16}C_{7}^{}+{}^{16}C_{6}^{}={}^{17}C_{7}^{}$